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- W4306999486 abstract "There is a known connection between the osp(1|2n) polynomial knot invariant $J_K^n$ and the so(2n+1) knot invariant ${}_{so} J_K^n$ studied by Clark in arXiv:1509.03533 and Blumen in arXiv:0901.3232. In the rank one case, the uncolored $U_{q}(osp(1|2))$ link invariant is equal to the $U_{t^{-1}q}(sl_2)$ link invariant where $t^2=-1$. We define a skein relation similar to the Kauffman bracket, and use that to recover an oriented link invariant which coincides with Clark's uncolored osp(1|2)-link invariant. This definition also comes from the representation theory of $U_{q,pi}(sl_2)$, but using different methods from Clark. We show that our invariant is easily categorified by a slightly modified version of Khovanov homology equipped with an extra $mathbb{Z}_4$-grading. We also construct a similarly modified version of Putyra's covering Khovanov homology from arXiv:1310.1895. This suggests that the similarity between the two invariants holds at the categorified level as well." @default.
- W4306999486 created "2022-10-22" @default.
- W4306999486 creator A5002252143 @default.
- W4306999486 date "2022-10-18" @default.
- W4306999486 modified "2023-09-23" @default.
- W4306999486 title "A new presentation of the osp(1|2)-polynomial link invariant and categorification" @default.
- W4306999486 doi "https://doi.org/10.48550/arxiv.2210.09583" @default.
- W4306999486 hasPublicationYear "2022" @default.
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